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Simplifying x2 + 18x = 108 Reorder the terms: 18x + x2 = 108 Solving 18x + x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + 18x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 18x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 18x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 18x + x2 = 0 + 108 18x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 18x + x2 = 108 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 108 + 81 Reorder the terms: 81 + 18x + x2 = 108 + 81 Combine like terms: 108 + 81 = 189 81 + 18x + x2 = 189 Factor a perfect square on the left side: (x + 9)(x + 9) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 9) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 9 = 13.747727085 Simplifying x + 9 = 13.747727085 Reorder the terms: 9 + x = 13.747727085 Solving 9 + x = 13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 13.747727085 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.747727085 + -9 x = 13.747727085 + -9 Combine like terms: 13.747727085 + -9 = 4.747727085 x = 4.747727085 Simplifying x = 4.747727085Subproblem 2
x + 9 = -13.747727085 Simplifying x + 9 = -13.747727085 Reorder the terms: 9 + x = -13.747727085 Solving 9 + x = -13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -13.747727085 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.747727085 + -9 x = -13.747727085 + -9 Combine like terms: -13.747727085 + -9 = -22.747727085 x = -22.747727085 Simplifying x = -22.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.747727085, -22.747727085}
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